How can I generate the nth term of a cubic sequence in the form of the nth term of a first order AP.... For example the nth term of a quadratic sequence is a+(n-1)d + ((n-1)(n-2)c/2) in terms of an AP where a=first term d=first difference (very first) c=second(Common) difference n=nth term. Now how can I generate one like that but for a cubic sequence?
Hey there! Ty for the useful vid!!... I just started my 9th grade as an IGCSE student and wanted to ask u for some advice on which all topics to follow closely and about paper pattern that I'll have to go for to give maths 0580 extended paper 2 & paper 4! Tysm.. pls revert to my comment
Hi dear... Glad to hear from you & I can see an enthusiastic student out there. Since you have just started with 0580, I would first recommend you to go through the syllabus document (Sharing the Link: cambridgeinternational.org/Images/597037-2023-2024-syllabus.pdf . www.cambridgeinternational.org/Images/597037-2023-2024-syllabus.pdf This will give you a clear idea about the assessment frameworks for Paper 2 & Paper 4. Now answering your question on what topics to focus & about the exam pattern: PAPER 2: You can expect about 20 to 22 Short Answer Questions. PAPER 4: You can expect about 10 to 11 Structured Questions(which means each question can have sub-parts ) 100% Sure Topic in PAPER 4 every year- -Graphical Solution of Functions (Link for your reference:czcams.com/video/1fdNb-_eIZI/video.html) -Functions & Inverse Functions(Link for your reference: czcams.com/video/B9h1h2WC2RY/video.html) Other topics seen in both the papers are given below: (Simple Interest, Compound Interest, Pythagoras Theorem , Circle Theorem, Solving Simultaneous Equations, Questions from Algebra(Simplify-Expand-Factorise-Use of Power rules), Direct & Inverse Proportion, Making the Subject , Solving Quadratic Equations, Straight line Equations, Sequences, Angle Sum Property, Transversal-Parallel lines & Angles formed, Word Problems from Percentages ,Ratio, Vectors, Sets, Probability & Venn Diagrams, Tree diagrams, Cumulative Frequency Curve, Grouped data- Mean, Median, Composite functions & Inverse of functions, Differentiation(Turning Points), Cosine Rule, Sine Rule, Area of triangle using the formula (0.5abSin C), Use of SOH-CAH-TOA, Questions based on Surface Area & Volume of 3D shapes, Sector & Segment Area, Sides-Area-Volume of Similar Shapes, Construction of Triangles etc.etc. I hope this will give you an overview of the focus points. But I always recommend my students not to skip any syllabus content if you want to get an A*. I am not sure what your expectations are , but keep it high. All the best to you & let me know if I can help you more. Abhi
Thankyou for your question. From the General form :Un=an^3+bn^2+cn+d Substituting for n=1, n=2, n=3 etc.. U1=a+b+c+d (This Equation is used to find d) U2=8a+4b+2c+d You can arrive at the conclusion that the first difference of the terms U2-U1= 7a+3b+c...............(1) (This Equation is used in the video as the Equation to find the c ) Similarly: U3=27a+9b+3c+d U4=64a+16b+4c+d You can arrive at the conclusion that the first difference of the terms U3-U2= 19a+5b+c .............(2) The second difference is the difference of the first difference, which is given by Eq(2) - Eq(1), 12a+2b--This is used in the video as the Equation to find b Following the same calculations further you can realize that the third difference is given by 6a. I hope this clarifies your question. Best Wishes!
Hi please watch the below link: czcams.com/video/wHdamYfPYM4/video.htmlsi=UNGGfQ5FhC61n855 It shows why and how I got these formulae. 6a =6 and so on. Thanks for your message.
It is better if you can explain why you come up with all those equation that you use for the 1st, 2nd and 3rd differences. People do not understand why are those equations are all of a sudden given. So a big part of solving the cubic sequence is missing. Apart from this everything else is very well explain.
czcams.com/video/wHdamYfPYM4/video.htmlsi=3XCV9PQXlVCsnSzd. Please watch this video of mine to see the explanation on why these equations are being used. Thanks for messaging me. Happy day to you!
How did you get "12a+2b" and "7a+3b+c"? Please, prove to us!!!
Sure! Will upload a video in few hours. Thanks for asking.
Sharing the answer for your question: czcams.com/video/wHdamYfPYM4/video.html . I hope it helps!
Nice
we have to frkn memorize these equations? thats hell man but u made it ez ty!
How can I generate the nth term of a cubic sequence in the form of the nth term of a first order AP....
For example the nth term of a quadratic sequence is a+(n-1)d + ((n-1)(n-2)c/2) in terms of an AP where
a=first term
d=first difference (very first)
c=second(Common) difference
n=nth term.
Now how can I generate one like that but for a cubic sequence?
Wow!
omg thank you so much i understand it
Glad to hear from you!
How do you acquire the sum of digits for quadratic and cubic sequence
Very helpful 🙏
Glad to hear this.
Job well done thank u so much
Glad to hear this!
Hey there! Ty for the useful vid!!...
I just started my 9th grade as an IGCSE student and wanted to ask u for some advice on which all topics to follow closely and about paper pattern that I'll have to go for to give maths 0580 extended paper 2 & paper 4! Tysm.. pls revert to my comment
Hi dear...
Glad to hear from you & I can see an enthusiastic student out there.
Since you have just started with 0580, I would first recommend you to go through the syllabus document (Sharing the Link: cambridgeinternational.org/Images/597037-2023-2024-syllabus.pdf
.
www.cambridgeinternational.org/Images/597037-2023-2024-syllabus.pdf
This will give you a clear idea about the assessment frameworks for Paper 2 & Paper 4.
Now answering your question on what topics to focus & about the exam pattern:
PAPER 2: You can expect about 20 to 22 Short Answer Questions.
PAPER 4: You can expect about 10 to 11 Structured Questions(which means each question can have sub-parts )
100% Sure Topic in PAPER 4 every year-
-Graphical Solution of Functions (Link for your reference:czcams.com/video/1fdNb-_eIZI/video.html)
-Functions & Inverse Functions(Link for your reference: czcams.com/video/B9h1h2WC2RY/video.html)
Other topics seen in both the papers are given below:
(Simple Interest, Compound Interest, Pythagoras Theorem , Circle Theorem, Solving Simultaneous Equations, Questions from Algebra(Simplify-Expand-Factorise-Use of Power rules), Direct & Inverse Proportion, Making the Subject , Solving Quadratic Equations, Straight line Equations, Sequences, Angle Sum Property, Transversal-Parallel lines & Angles formed, Word Problems from Percentages ,Ratio, Vectors, Sets, Probability & Venn Diagrams, Tree diagrams, Cumulative Frequency Curve, Grouped data- Mean, Median, Composite functions & Inverse of functions, Differentiation(Turning Points), Cosine Rule, Sine Rule, Area of triangle using the formula (0.5abSin C), Use of SOH-CAH-TOA, Questions based on Surface Area & Volume of 3D shapes, Sector & Segment Area, Sides-Area-Volume of Similar Shapes, Construction of Triangles etc.etc.
I hope this will give you an overview of the focus points. But I always recommend my students not to skip any syllabus content if you want to get an A*. I am not sure what your expectations are , but keep it high.
All the best to you & let me know if I can help you more.
Abhi
@@sheghsmath Tsym! I'm sure I'll be able to get an a*!
Where did you get the 7a+3b+c from and likewise the 12a+2b.Thank you
Thankyou for your question.
From the General form :Un=an^3+bn^2+cn+d
Substituting for n=1, n=2, n=3 etc..
U1=a+b+c+d (This Equation is used to find d)
U2=8a+4b+2c+d
You can arrive at the conclusion that the first difference of the terms U2-U1= 7a+3b+c...............(1)
(This Equation is used in the video as the Equation to find the c )
Similarly:
U3=27a+9b+3c+d
U4=64a+16b+4c+d
You can arrive at the conclusion that the first difference of the terms U3-U2= 19a+5b+c .............(2)
The second difference is the difference of the first difference,
which is given by Eq(2) - Eq(1),
12a+2b--This is used in the video as the Equation to find b
Following the same calculations further you can realize that the third difference is given by 6a.
I hope this clarifies your question. Best Wishes!
@@sheghsmath isn't it U4=*64*a+16b+4c+d??
@@prettylife6472 my quick typing went wrong! Thanks for your message, it is4^3= 64 & not 34.
@@sheghsmath oh it's totally okay I understand,by the way your video really helped me so thanks a lot and have a good day
and my teacher wanted to make me draw a table for this, hahah hell nah this is way quicker
Suiiiiii
How are you get 6a=6 then a=1 and 12a+2b=16?
Hi please watch the below link:
czcams.com/video/wHdamYfPYM4/video.htmlsi=UNGGfQ5FhC61n855
It shows why and how I got these formulae. 6a =6 and so on. Thanks for your message.
@hanspierre8272 Hope your doubt is clarified in this video.
czcams.com/video/wHdamYfPYM4/video.htmlsi=UNGGfQ5FhC61n855
I did not understand. From where you got 12a+2b and other equations? 😭
It is the rule for it, its for all cubic sequences i think :)
Sharing the explanation for your question. czcams.com/video/wHdamYfPYM4/video.html
It is better if you can explain why you come up with all those equation that you use for the 1st, 2nd and 3rd differences. People do not understand why are those equations are all of a sudden given. So a big part of solving the cubic sequence is missing. Apart from this everything else is very well explain.
czcams.com/video/wHdamYfPYM4/video.htmlsi=3XCV9PQXlVCsnSzd. Please watch this video of mine to see the explanation on why these equations are being used.
Thanks for messaging me. Happy day to you!
Why is 6A=6?
Apart of the formula, which isnt shown in this video unfortunately
Sorry it is shown, the equations she lists to the left at 4:56 are the formulas
Didn’t explain anythign bro my test is in 30 minutes